Abstract.
In the attempt to define P systems with the communication of objects through membranes controlled in an as simple as possible manner, we consider the case of string-objects (processed by rewriting or by splicing) with immediate communication: the string obtained by applying an evolution rule is immediately moved from the region where it is obtained to one of the neighboring regions, nondeterministically chosen. Rewriting P systems of this type (and without other controls on the communication or the rule application) are shown to generate only matrix languages, while for splicing P systems we obtain again the usual result from membrane system area: computational universality (that is, a characterization of recursively enumerable languages).
*Work supported by a grant of NATO Science Committee, Spain, 2000--2001, and by Facultad de Informatica, Universidad Politecnica de Madrid.
**Work supported by Turku Center for Computer Science, Finland, and by a grand of Facultad de Informatica, Universidad Politecnica de Madrid.